Math worksheet with rational expression problems and solutions, designed for algebra practice.

Since no specific problem was selected from the worksheet, I will solve Problem #1 as a representative example to demonstrate how to simplify rational expressions with like denominators.

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Problem 1:
Simplify:
\[
\frac{u - v}{8v} + \frac{6u - 3v}{8v}
\]

Step-by-step reasoning:

We are adding two fractions that have the same denominator: \(8v\).
When denominators are the same, we can combine the numerators directly over the common denominator.

So:

\[
\frac{(u - v) + (6u - 3v)}{8v}
\]

Now combine like terms in the numerator:

- \(u + 6u = 7u\)
- \(-v - 3v = -4v\)

So the numerator becomes: \(7u - 4v\)

Thus, the simplified expression is:

\[
\frac{7u - 4v}{8v}
\]

Check if anything cancels — there’s no common factor between numerator and denominator (since \(7u - 4v\) doesn’t share a factor with \(8v\) unless specific values are given), so this is fully simplified.

✔ This matches the red answer shown on the worksheet.

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Final Answer:
\[
\frac{7u - 4v}{8v}
\]